Gearing for my South Bend Junior Lathe

The Formula
Diametral Pitch Calculator
Calculating Gearing for a Specific Threads-Per-Inch
Calculate Threads-Per-Inch from Two Gears

I finally had an opportunity to look at some measurements for change gears.  I knew I needed to - I had seen multiple types of gears for things labeled "original South Bend".  Some were 18DP (diametral pitch), while rare ones were 16DP.  Some had 9/16" bores, while some had 5/8" bores.  The 16DP 5/8" bore change gear sets are rare on eBay (I've been watching, just in case).  There were some 18DP 5/8" bore gear sets, and 18DP 9/16" bore gear sets, but I have yet to see a set of 16DP 5/8" bore sets since I have had the lathe.

Rumors abound that my lathe was the 5/8" bore 16DP gears.  I believe in the mid 1930's, they started moving to the 18DP gears, and then changed the bore at the end of the 1930's when they introduced the "workshop" and "toolroom" models.

I knew I needed to make sure, just in case I saw them, so that I could buy them the spot.

So, I had to grab some measurements.  I needed to identify the diametral pitch of the gear.  You do this by obtaining the number of teeth on the gear, and the diameter of the outside edge (where the teeth get to, not the bottom of the teeth).  The stud gear that drives the idler gear is 1 and 1/8" across, and there are 16 teeth on it.  The bore is (indeed) 5/8".  The formula is :

Diametral Pitch =	(Number of Teeth + 2)
	Diameter of gear in inches

This gave me :

Diametral Pitch =	(16 + 2)
	1.125

And that resulted in a 16DP gear.  Now, when it comes to gears, there are a whole lot of equations.  However, one other field that is required is called the pressure angle.  Fortunately, I believe South Bend only made 16DP gears in the standard 14.5 degree pressure angle, so that tells me exactly what I need to know :

Diametral Pitch :	16
Teeth :	16
Diameter :	1.125
Bore :	5/8"
Pressure Angle :	14.5

Now I just need to buy the set when the rare show up, or cut my own.  I did find out how to determine the pitch based on the gearing, using an old threading chart :

Here's the formula, spot checked all over that threading chart :

Thread Pitch =	screw gear teeth	* 8
	stud gear teeth

For example :

30 =	60	* 8
	16

As a result, you can create a new pitch not listed (e.g. a metric pitch) by plugging in a few numbers until you get rounded numbers, e.g. a 39 threads-per-inch would be :

39 =	78	* 8
	16

So, if I wanted to cut 39 TPI, I'd slap a 16-tooth gear on the stud, and a 78-tooth gear on the lead screw.  Isn't math, science, and engineering fun?  FYI, I threw it into a fast chunk of perl to find that 39TPI, just for kicks :

my $tpi = 39;
my @try_first = (64, 32, 16, 20, 44, 48, 72, 56, 40, 80, 72, 52);
my $stud_gear = undef;
my $screw_gear = undef;
my @stud_gears = @try_first;
my $gear = 16;
while (!defined($screw_gear) && (!defined($stud_gear))) {
  my $stud = shift(@stud_gears);
  if (!defined($stud)) {
    $stud = $gear;
    $gear++;
    if ($gear > 80) {
      $screw_gear = -1;
      $stud_gear = -1;
    };
  };
  my $screw = ($tpi / 8) * $stud;
  if (int($screw) == $screw) {
    print "screw = $screw, stud = $stud = $tpi TPI\n";
  };
};

I know it's lazy code, and rather poorly done, but for an 8-minute "see if I can make it work", it did pretty good! Not the best, but it worked as well as intended.

I also threw the above code into some javascript to see if I could do this in the blog, and it does work :

Diametral Pitch
Outside Diameter	:
Number of Teeth	:
Diametral Pitch	:
Circular Pitch
Circular Pitch	:
Pressure Angle
Base Pitch	:
Pressure Angle	:

Calculating Gearing for a Specific Threads-Per-Inch
Yes, I am editing this blog post - because I thought, "If my dad asks if I can cut a screw for him on his old car, can I calculate the gears to make it happen?" That blossomed into the desire to add a calculator for what gears would be needed on the web, specific to the South Bend Junior.

Threads-Per-Inch :

*note - this could take a while, and may look like the browser locks up*

 

Calculate Threads-Per-Inch from Two Gears

While I was at it, I thought I'd throw one more calculator onto the post - one to get the threads-per-inch when given two gears.

Screw Gear :
Stud Gear :

And something to take two gears and calculate the TPI.